Math Is AWESOME!

I truly enjoyed creating Untied, with its free-form, no math construction. Though I used a ruler for parts of it, it wasn’t because the outcome depended on the measurement. Instead, at those instances I was only interested in straight, and sometimes parallel, lines.

However, I love the challenge of a technically difficult quilt, too. For a change of pace, I began a brand new project. The inspiration for it is a piece of fabric I bought several years ago. It’s a fussy historical print that I’ve always loved. However, it’s fussy and historical, and the colors are just off, all of which have made it hard to use. If it is cut into small patches, the impact of the print disappears, but large pieces would require designing just for it. So I am.

I started by pulling from stash, which is how almost all my quilts begin. I pulled all the blues that could work with that print, which meant they had to have a tinge of green and a little grey. It’s the color I learned as French blue. As it turns out, I don’t have a lot of blue with that, and all of it is in scraps or small pieces, other than the inspiration print. We’ll see how far I get before needing to buy something.

Burgundy reds, creams, browns, and cheddar oranges also came out of stash, including from my scrap drawer. I’m trying to commit to using my scraps more effectively. They come in handy, as I’ll explain later.

My center block is 18″ finished. I knew I wanted to turn it on point twice. The method is exactly the same as used for the economy block setting. This is also called “square in a square.”

And this is where the first round of harder quilt math comes in. (It’s not very hard, just a thing to learn, or store so you can look it up.) As noted in the linked post, when setting a square on point twice, the finished size of the resulting block is twice the dimensions of the initial finished square. For my 18″ block, I would end up with a 36″ center, once trimmed and finished. (See below for the calculation and reason why.)

What a great way to quickly increase the size of a quilt!

After trimming, I added a 1″ border all the way around, taking it to 38″ square. That’s an odd size.

Options for a 36″ Edge
Most quilt blocks are square, or are rectangular with length twice the width, like flying geese blocks. I typically divide a border length into a number of equal increments to find how many blocks could fit along the edge. For example, if I put a block border directly along the 36″ center, I would divide 36 in various ways to get possibilities. Let’s start with whole inches.
36/18 = 2. I could have 18 blocks measuring 2″.
36/12 = 3. I could have 12 blocks measuring 3″.
36/9 = 4. I could have 9 blocks measuring 4″.
36/6 = 6. I could have 6 blocks measuring 6″.
But remember we could also go to half-inches, such as
36/8 = 4.5. I could have 8 blocks measuring 4.5″.
36/24 = 1.5. I could have 24 blocks measuring 1.5″.

You can see there are actually infinite variations, though I like to stick to the ones that are easy to construct.

Options for a 38″ Edge
But I didn’t want to put a block border directly against the large center. I wanted the hard line of a narrow border before anything else, to contain the pale toile. That gave me 38″, which is harder to divide nicely than 36″.
38/19 = 2. I could have 19 blocks measuring 2″, but this was too narrow to work well with the proportions of the center. And 19 is a prime number, so I couldn’t subdivide it into whole numbers.
I could shift to fractionals, such as
38/8 = 4.75. Sure… This actually would work fine with something like HST or hourglasses.

My go-to blocks are half-square triangles and hourglasses. I don’t want this quilt to look like others I’ve made, so it’s good to try something different.

Then I had a thought, a math thought! What if I divide 38 by 1.414? (That actually was the first thought. Then I thought…) If I turn blocks on point rather than set them straight, I would need to know the number of blocks using the math for the diagonal.

Here’s the concept. The picture below shows a triangle that is 1″ on the vertical and horizontal sides. The diagonal measures 1.414″, which is the square root of 2″. (Check with your calculator if you don’t believe me.)

Pythagorean Theorem
For a right triangle, the square of the length of the diagonal (hypotenuse) is equal to the sum of the squares of the other two sides. We often see this expressed as a² + b² = c². To find c, take the square root of c².

In the case to the left, a = 1; b = 1; c is the square root of 2, or 1.414.

In fact, the diagonal of every square is 1.414 times the length of the side. Solength x 1.414 = diagonal
1″ x 1.414 = 1.414″
2″ x 1.414 = 2.828″ or close to 2 7/8″
3″ x 1.414 = 4.242″ or close to 4 1/4″
4″ x 1.414 = 5.656″ or close to 5 5/8″
and so on.

That also means that if I know the diagonal of a square, I can find the length usingdiagonal/1.414 = length. For example
6″/1.414 = 4.243″, or very close to 4 1/4″.38″/1.414 = 26.875″. Hooray!!

Huh? Why is that good? 26.875 is very close to 27, which is a very easy number to use. For instance,
27/9 = 3.

I could use 9 blocks measuring 3″, turned on point. (There were other options, too, such as 6 blocks at 4.5″.)

3 x 1.414 = 4.242, the diagonal of a 3″ square, and the width of a 3″ block when turned on point.
4.242 x 9 = 38.178, or very close to 38″.

So if I use 9 3″ blocks turned on point, I’ll have the length needed for a 38″ border.

(And to review the concept in another way, let’s go back to the 18″ block. When I turn it on point twice, I’m doing this: 18″ x 1.414 = 25.452″ 25.452″ x 1.414 = 36″. This is the same as 18″ x 1.414² = 18″ x 2 = 36″.)

I chose to use the historical print and other blue scraps as the 3″ finish squares. For the background fabric, a light background would give good value contrast for the blues so they stand out well. I picked a pink and tan print on pale cream. The pink works because the reds have a pink cast. Right now I’m still working completely from stash and scraps. I was able to cut most of the setting triangles from a couple of larger pieces, but for the last few I had to sew scraps together to cut patches.

Can you find the seams where the setting fabric scraps had to be sewn together?

With the on-point border added, my current center is 46.5″ finished, another weird number. I plan to add an unpieced strip next, but I haven’t decided its width. I could add a strip to take it to 48″, 49″, 50″… So the next design decision, really, is the border after that, which will determine the width of the strip.

I feel really fortunate to have the math skills as part of my craft toolbox. You can make beautiful quilts without knowing how to do any of this, but knowing increases the options open to me. Math is awesome!

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23 thoughts on “Math Is AWESOME!”

You have some really great coordinating fabrics! I love working to showcase a great print and enjoyed reading about your approach. I love the pattern you have going. I have probably used more math since I started quilting than I had after high school for anything else.

I took a lot of math in college, ironic considering how little I had in high school. And as an investment manager and finance instructor, I used it all the time. This is more fun. 🙂 Thanks for taking a look. I do like these fabrics together and can’t wait to see what they make.

I’m going to bookmark this! I don’t tend to come up with designs that involve a lot of triangles, so I have managed to avoid too much complex calculation, but it’s handy to know where to find the resources when I need them. And yes, I can see the seams, but I had to look to find them!

Of course half-square triangles set just as squares don’t take much calculation, other than enough to cut the patches. It’s really when you set squares on point where all this comes in. I might end up rewriting a lot of this as just a math tutorial, taking the project out of it. That would make it easier to dig through. And yes, I hid most of those seams well, but there were 2 that, because of the direction of the print I had available, just couldn’t be hidden. Thanks.

You weren’t kidding when you said you were going to tell us more about process! I have to admit my eyes glazed over a bit but I can see how valuable this knowledge could be. And it all made me think of a song called “New Math” by comedian Tom Lehrer–have you heard of him?

No doubt, and no shame admitting your eyes glazed over! Mine would, too! I hadn’t heard of Tom Lehrer but listened to his song. Jim had heard it before. I looked up the wiki bio and my goodness, what an amazing man!!! https://en.wikipedia.org/wiki/Tom_Lehrer

New Math from the 60s. These days it would be Common Core and at least as confusing!

Oo! Maths terrifies me – my brain goes into ‘lock down’ and I just have to look away! Thankfully that doesn’t mean patchwork becomes inaccessible ☺and I trust the work of design mathematicians like yourself to see me through the tricky bits! The quilt top looks beautiful, those subtle ‘off’ colours look very comforting and homey.

I have to admit your comment makes me sad. I think it’s true for many people that they’re sure they can’t do the calculations. As a designer I couldn’t do a lot of what I do without the math, but it sounds like you’ve figured how to work around it.

Thanks for the comments on the quilt. Still a work in process! Today I actually sewed on those borders of squares on point. I had them prepped when I posted yesterday. They look pretty good, but the dilemma is — what next?!?

For blocks like this one I start making brown paper templates because I need to actually see how the math would work out. Then, I measure the templates once I’m happy with the fit and cut my fabric. Otherwise, I spend way too much time double checking my math.

Funny thing…math was not my strong suite in school. Then in college it all clicked together. Little did I know that I would end up in a job that solely relied on math! Good post and yes I will use your method of calculating.. I must admit, I’ve always been a “wing it” type person, but have found with quilting. .sometimes it works and sometimes it doesn’t. The last deer quilt was a “wing it” project, just designing as I went..must admit I liked it the best. Your design is perfect and like the way you used the French blue color…thinking I need to start a new project and get my creative juices going. …

Your comment posted twice so I deleted one. 🙂 Yes, I enjoy winging it, too, but it can be either more stressful or more fun. Untied is winging it, mostly fun, as the sizing didn’t matter. But there was some stress in cutting fabrics that would be hard to replace. For this one, The stress is in making the math work numerically, and also making it work for the fabrics I have. But the fun is in having those things work out. I’m not willing to give up either way of working. Fortunately I don’t have to!

l love what you do with the fabrics here, the ‘wandering sage’ fabric in centre brings out the chrysanthemums in your French blue [powder blue in England l think?] in particular, brilliant! The ‘make it easier if l divide by 1.414’ made me laugh out loud, l am too brain fogged by fibro to stand a chance with that, l would have added a narrow border of 1 1/2″, thus ending with 39″, easy to divide by 3… many roads to Rome 😉 but l love that YOU opted for that, like you say, math IS awesome!

This is a great post…setting squares on point has never really been my easiest task. I use the Robert Kaufman app but you can’t go beyond 18″ I think so it would be nice to try out your method 🙂 And yes I don’t feel too bad now about having to do maths up until the end of my first degree

I’ll admit it took me a long time to really understand why this works. For as much financial math and statistics as I’ve done, geometry is not something I learned well. So yes, *relationships* is what it takes me to understand the construction.

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